Friday Puzzler -- Cake and Box

Alex Y
A geometry teacher decided to have an unusual cake baked for the year-end party for his class. He asked the bakery to prepare a triangular cake with three unequal sides, the measurements of which he specified. The baker ordered a box for the cake with the same three side lengths.

After he made and iced the cake, the baker pulled out the box he was given and discovered that while the sides were the same length, they were in the wrong order, so that the box was a mirror image of the cake. The cake was iced, so flipping it over to put in the box was not an option. He called the geometry teacher to ask what to do. The teacher said not to worry, and described how the cake could be cut into three pieces, which could be reassembled in the box.

How did that work?

This is a puzzle in two dimensions, so don't waste your time looking for solutions involving the thickness of the cake (although hats off to you if you find such a solution!)

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